What is the domain and derivative of f(x)=ln(2xsqrt(2+x))?
1 answer:
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The unknown b is stuck in the exponent position.
We can can fix that by using logarithms.
Log is the inverse operation of the exponential.
We'll take log of each side.
Log of what base tho?
Well, the base of our exponential is e,
so we'll take log base e of each side.
We'll apply one of our log rules next:
This allows us to take the exponent out of the log,
Another thing to remember about logs:
When the base of the log matches the inside of the log,
then the whole thing is simply 1,
So our equation simplifies to this,
As a final step, divide both sides by 3,
k, hope that helps!
Complete question:
Anty was riding his bike to school at a speed of 12 mph. When he was <u>half </u>of the way there, he got a flat tire. His mother drove him the rest of the way at a speed of 48 mph. What was his average speed?
Answer:
His average speed is 19.2 mph
Step-by-step explanation:
Given;
speed of Anty to school half of the way, v₁ = 12 mph
speed of Anty when his mother drove him half of the way, v₂ = 48 mph
The average speed of Anty is calculated as;
The value of the average speed is closer to 12 mph than 48 mph because Anty spent more time moving at 12 mph than at 48 mph.
Let the equal distance travel at each speed = 96 miles
Time taken at 12 mph =
Time taken at 12 mph =
Average speed =
Also, you can assume any other equal distance traveled at each speed, the average speed will still be 19.2 mph.
<u>Check:</u> let the equal distance traveled at each speed = 480 miles
Time taken at 12 mph = 480/12 = 40 hours
Time taken at 48 mph = 480/ 48 = 10 hours
Average speed = (480 + 480) / (40 + 10)
= 19.2 mph